Flux-tube patterns in the Ginzburg-Landau model of type-I superconductors

We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields.
We determine the optimal scaling law of the minimal energy in terms of the parameters of the problem, when the applied magnetic field is sufficiently small and the sample sufficiently thick.
We show that, in an appropriate asymptotic regime, flux patterns may be described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via Gamma-convergence.
This talk is bases on joint work with Michael Goldman, Felix Otto and Sylvia Serfaty.